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BMI, or Body Mass Index, is a measurement that assesses body fat based on height and weight, with a high BMI increasing the risk for certain diseases. It is calculated by dividing weight in kilograms by height in meters squared. For example, to calculate the BMI of someone weighing 175 pounds and standing 5 feet 9 inches tall, first convert weight: 175 pounds equals 79.38 kilograms (using 1 pound = 0.4536 kg). Next, convert height: 5 feet 9 inches equals 69 inches, which is 1.75 meters (using 1 inch = 0.0254 m). The BMI formula then gives a result of 25.8. The video also provides a formula for BMI using pounds and inches, alongside a weight classification chart.